U.S. patent application number 11/250747 was filed with the patent office on 2006-04-20 for resonator, light emitting device, and wavelength conversion device.
This patent application is currently assigned to Canon Kabushiki Kaisha. Invention is credited to Hikaru Hoshi, Kiyokatsu Ikemoto, Akinari Takagi.
Application Number | 20060083477 11/250747 |
Document ID | / |
Family ID | 35610241 |
Filed Date | 2006-04-20 |
United States Patent
Application |
20060083477 |
Kind Code |
A1 |
Takagi; Akinari ; et
al. |
April 20, 2006 |
Resonator, light emitting device, and wavelength conversion
device
Abstract
A resonator is provided which is produced by a defect formed in
a three-dimensional photonic crystal. The three-dimensional
photonic crystal can include layers containing a plurality of
columnar structures with discrete structures in sublayers.
Inventors: |
Takagi; Akinari;
(Utsunomiya-shi, JP) ; Hoshi; Hikaru;
(Utsunomiya-shi, JP) ; Ikemoto; Kiyokatsu;
(Utsunomiya-shi, JP) |
Correspondence
Address: |
Canon U.S.A. Inc.;Intellectual Property Division
15975 Alton Parkway
Irvine
CA
92618-3731
US
|
Assignee: |
Canon Kabushiki Kaisha
Ohta-ku
JP
|
Family ID: |
35610241 |
Appl. No.: |
11/250747 |
Filed: |
October 14, 2005 |
Current U.S.
Class: |
385/147 |
Current CPC
Class: |
B82Y 20/00 20130101;
H01S 5/10 20130101; G02B 6/1225 20130101 |
Class at
Publication: |
385/147 |
International
Class: |
G02B 6/00 20060101
G02B006/00 |
Foreign Application Data
Date |
Code |
Application Number |
Oct 15, 2004 |
JP |
2004-301374 |
Claims
1. A resonator including a point defect formed in a
three-dimensional photonic crystal, the three-dimensional photonic
crystal comprising: a first layer including a plurality of columnar
structures spaced apart by a first predetermined interval; a second
layer including a plurality of columnar structures spaced apart by
a second predetermined interval, the columnar structures extending
in a direction different from that of the columnar structures in
the first layer; a third layer including a plurality of columnar
structures spaced apart by a first predetermined interval, the
columnar structures extending in the same direction as that of the
columnar structures in the first layer; and a fourth layer
including a plurality of columnar structures spaced apart by a
second predetermined interval, the columnar structures extending in
the same direction as that of the columnar structures in the second
layer; wherein the first to fourth layers are stacked sequentially,
the first layer and the third layer are stacked such that the
columnar structures contained in the two layers are mutually
shifted by one-half the first predetermined interval in the
direction, in the layers, perpendicular to the direction of the
extension of the columnar structures, the second layer and the
fourth layer are stacked such that the columnar structures
contained in the two layers mutually shift by one-half the second
predetermined interval in the direction, in the layers,
perpendicular to the direction of the extension of the columnar
structures, and wherein the point defect has a thickness different
from the each thickness of the four layers.
2. The resonator according to claim 1, wherein the columnar
structures of the first layer are orthogonal to the columnar
structures of the second layer.
3. The resonator according to claim 1, wherein the first and second
predetermined intervals are equal.
4. The resonator according to claim 1, wherein the point defect is
of a medium different from the medium of the columnar
structures.
5. The resonator according to claim 1, wherein the point defect is
of the same medium as the columnar structures.
6. The resonator according to claim 1, wherein the point defect is
disposed such that the center of the point defect lies on an axis
extending in the stacking direction of the layers from the center
of an intersection of projections of the columnar structures.
7. The resonator according to claim 1, wherein the point defect is
disposed such that the center of the point defect lies on an axis
extending in the stacking direction of the layers from a position
shifted by one-half of the predetermined interval in either of the
directions in which the columnar structures are arranged in a plane
perpendicular to the stacking direction, from the center of an
intersection of projections of the columnar structures.
8. The resonator according to claim 1, wherein the resonator
operates in a single mode.
9. A light emitting device comprising: the resonator according to
claim 1; and excitation device for exciting an active medium that
emits light, wherein the resonator contains the active medium.
10. A wavelength conversion device comprising the resonator
according to claim 1, wherein the resonator contains a nonlinear
material.
11. The resonator according to claim 1, wherein the resonator
serves as a wavelength selection filter.
12. A resonator including a point defect formed in a
three-dimensional photonic crystal, the three-dimensional photonic
crystal comprising: a first layer including a plurality of columnar
structures spaced apart by a first predetermined interval; a second
layer including a plurality of columnar structures spaced apart by
a second predetermined interval, the columnar structures extending
in a direction different from that of the columnar structures in
the first layer; a third layer including a plurality of columnar
structures spaced apart by a first predetermined interval, the
columnar structures extending in the same direction as that of the
columnar structures in the first layer; a fourth layer including a
plurality of columnar structures spaced apart by a second
predetermined interval, the columnar structures extending in the
same direction as that of the columnar structures in the second
layer; and additional layers, each including at least one sublayer
containing discrete structures disposed discretely in a plane
parallel to each of the four layers, wherein the first to fourth
layers are stacked sequentially with the additional layer between
the adjacent two layers thereof, the first layer and the third
layer are stacked such that the columnar structures contained in
the two layers are mutually shifted by one-half the first
predetermined interval in the direction, in the layers,
perpendicular to the direction of the extension of the columnar
structures, the second layer and the fourth layer are stacked such
that the columnar structures contained in the two layers mutually
shift by one-half the second predetermined interval in a direction
perpendicular to the direction of the extension of the columnar
structures, discrete structures contained in the additional layers
are disposed at the positions corresponding to the intersections of
the columnar structures, and wherein the point defect is formed
including at least one of the sublayers containing the discrete
structures.
13. The resonator according to claim 12, wherein each additional
layer includes at least two sublayers containing the discrete
structures.
14. The resonator according to claim 12, wherein the columnar
structures of the first layer are orthogonal to the columnar
structures of the second layer.
15. The resonator according to claim 12, wherein the first and
second predetermined intervals are equal.
16. The resonator according to claim 12, wherein the point defect
is formed only in at least one sublayer containing the discrete
structures.
17. The resonator according to claim 12, wherein the point defect
is formed in one of the layers containing the columnar structures
and the adjacent sublayer containing the discrete structures.
18. The resonator according to claim 12, wherein the point defect
is of a medium different from the medium of the columnar
structures.
19. The resonator according to claim 12, wherein the point defect
is of the same medium as the columnar structures.
20. The resonator according to claim 12, wherein the point defect
is disposed such that the center of the point defect lies on an
axis extending in the stacking direction of the layers from the
center of an intersection of projections of the columnar
structures.
21. The resonator according to any one of claims 12, wherein the
point defect is disposed such that the center of the point defect
lies on an axis extending in the stacking direction of the layers
from a position shifted by one-half of the predetermined interval
in either of the directions in which the columnar structures are
arranged in a plane perpendicular to the stacking direction, from
the center of an intersection of projections of the columnar
structures.
22. The resonator according to claim 12, wherein the resonator
operates in a single mode.
23. A light emitting device comprising: the resonator according to
claim 12; and an excitation device for exciting an active medium
that emits light, wherein the resonator contains the active
medium.
24. A wavelength conversion device comprising the resonator
according to claim 12, wherein the resonator contains a nonlinear
material.
25. The resonator according to claim 12, wherein the resonator
serves as a wavelength selection filter.
Description
BACKGROUND OF THE INVENTION
[0001] 1. Field of the Invention
[0002] The present invention relates to a resonator using a
three-dimensional photonic crystal, more particularly, though not
exclusively, the present invention relates to a resonator formed
from a defect in a photonic crystal.
[0003] 2. Description of the Related Art
[0004] Yablonovitch has proposed an idea of controlling the
transmission and reflection characteristics of electromagnetic
waves by structures smaller than or equal to a wavelength in
Physical Review Letters, Vol. 58, p. 2059, 1987. This document has
taught that the transmission and reflection characteristics of
electromagnetic waves can be controlled by periodically arranging
structures smaller than or equal to a wavelength. A photonic
crystal can be such a unit of periodically arranged structures, and
suggests that a reflection mirror exhibiting no optical loss,
namely, a reflectance of about 100%, can be achieved in a specific
wavelength region. This region is referred to as a photonic band
gap, likened to an energy gap of a semiconductor. In particular, a
three-dimensional microscopic periodic structure can produce a
photonic band gap for all the light entering from any direction
(hereinafter referred to as complete photonic band gap). The
complete photonic band gap can have various applications (e.g.,
light emitting devices, control of spontaneous emission).
[0005] Woodpile structures in which columnar structures are
periodically stacked in a layered manner have been discussed in,
for example, U.S. Pat. No. 5,335,240 and Japanese Patent Laid-Open
No. 2004-6567. Japanese Patent Laid-Open No. 2004-6567 has also
discussed a resonator using a woodpile structure having a defect
inside. The defect is formed in a rectangular solid shape with the
same thickness as that of the columnar structure, and is present
among the columnar structures. In general, a resonator produced by
a defect formed in a photonic crystal has plural resonance modes.
Resonators used in light emitting devices or wavelength selection
filters have designed confinement effects and satisfy resonance
requirements for a designed resonant wavelength. In addition, in
order to avoid the influence of other resonance modes having a
wavelength close to the designed wavelength, for example, to reduce
the effect of mode hopping in a laser, one can provide a large
difference between the designed resonant wavelength and the
wavelengths of the resonant in the other resonance modes.
[0006] The periodicity around the defect of the periodic structure
can be increased to increase the reflectance. Japanese Patent
Laid-Open No. 2004-6567 has also discussed another approach in
which the difference in resonant wavelength between adjacent
resonance modes is controlled by varying the lengths of two sides
other than the thickness of rectangular solid defect, and by
shifting the position of the defect with respect to the columnar
structures. Unfortunately, the shift of the position of the defect
makes the periodic structure asymmetrical, so that the energy
distribution of the electromagnetic field in the resonator is also
made asymmetrical. If the resonator is used in a laser, such
asymmetry causes a large deflection of the orientation of the
emitted light and may result in a critical problem. In addition,
the maximum of the shift in the position of the defect is 1/4 of
the period of columnar structure arrangement, making the choices of
designed resonant wavelength limited.
SUMMARY OF THE INVENTION
[0007] Accordingly, an exemplary embodiment is directed to a
resonator resonating in a single mode with a symmetrical energy
distribution of an electromagnetic field.
[0008] At least one exemplary embodiment is directed to a
resonator, which can be by a point defect formed in a
three-dimensional photonic crystal. The three-dimensional photonic
crystal can include a first layer to a fourth layer. The first
layer includes a plurality of columnar structures spaced apart by a
first predetermined interval. The second layer includes a plurality
of columnar structures spaced apart by a second predetermined
interval, the columnar structures of the second layer extending in
a direction different from that of the columnar structures in the
first layer. The third layer includes a plurality of columnar
structures spaced apart by a third predetermined interval, the
columnar structures of the third layer extending in about the same
direction as that of the columnar structures in the first layer.
The fourth layer includes a plurality of columnar structures spaced
apart by a fourth predetermined interval, the columnar structures
extending in substantially the same direction as that of the
columnar structures in the second layer. The first to fourth layers
can be stacked such that the columnar structures of the first layer
are shifted by about half of the regular interval in the direction
substantially perpendicular to the direction of the extension of
the columnar structures of the first and third layers, and such
that the columnar structures of the second layer are shifted by
about half of the regular interval in the direction perpendicular
to the direction of the extension of the columnar structures of the
fourth layer. The point defect can have a thickness different from
each thickness of the four layers.
[0009] Further features of the present invention will become
apparent from the following description of exemplary embodiments
with reference to the attached drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
[0010] FIG. 1 illustrates a schematic illustration of a resonator
using a three-dimensional photonic crystal according to a first
exemplary embodiment.
[0011] FIG. 2 illustrates schematic xy sectional views of layers of
the resonator shown in FIG. 1.
[0012] FIG. 3 illustrates an enlarged view of a region around a
point defect of the resonator shown in FIG. 1.
[0013] FIG. 4 illustrates a graph showing a photonic band structure
according to the first exemplary embodiment.
[0014] FIG. 5 illustrates a graph showing the relationship between
the defect mode frequencies and the length Dx, in the x-axis
direction, of the point defect according to the first exemplary
embodiment.
[0015] FIG. 6 illustrates a graph showing the relationship between
the defect mode frequencies and the length Dy, in the y-axis
direction, of the point defect according to the first exemplary
embodiment.
[0016] FIG. 7 illustrates a graph showing the relationship between
the defect mode frequencies and the thickness Dz of the point
defect according to the first exemplary embodiment.
[0017] FIG. 8 illustrates a spectrum of defect mode frequency
according to the first exemplary embodiment.
[0018] FIG. 9 illustrates a defect mode pattern of an xy section
according to the first exemplary embodiment.
[0019] FIGS. 10A and 10B illustrate schematic representations of
point defect arrangements.
[0020] FIG. 11 illustrates a schematic representation of a
resonator using a three-dimensional photonic crystal according to a
second exemplary embodiment.
[0021] FIG. 12 illustrates an enlarged view of a region around a
point defect of the resonator shown in FIG. 11.
[0022] FIG. 13 illustrates a graph showing a photonic band
structure according to the second exemplary embodiment.
[0023] FIG. 14 illustrates a graph showing the relationship between
the defect mode frequencies and the length Dx, in the x-axis
direction, of the point defect according to the second exemplary
embodiment.
[0024] FIG. 15 illustrates a graph showing the relationship between
the defect mode frequencies and the length Dy, in the y-axis
direction, of the point defect according to the second exemplary
embodiment.
[0025] FIG. 16 illustrates a graph showing the relationship between
the defect mode frequencies and the thickness Dz of the point
defect according to the second exemplary embodiment.
[0026] FIG. 17 illustrates a spectrum of a defect mode according to
the second exemplary embodiment.
[0027] FIG. 18 illustrates a defect mode pattern of a xy section
according to the second exemplary embodiment.
[0028] FIG. 19 illustrates a schematic representation of a laser
device.
[0029] FIG. 20 illustrates a schematic representation of a
wavelength conversion device.
DESCRIPTION OF THE EMBODIMENTS
[0030] The following description of at least one of the possible
exemplary embodiment(s) is merely illustrative in nature and is in
no way intended to limit the invention, its application, its
equivalents, or uses.
[0031] Processes, techniques, apparatus, and materials as known by
one of ordinary skill in the art may not be discussed in detail but
are intended to be part of the enabling description where
appropriate. For example some examples of photonic crystal
formation are discussed, equivalents and other photonic crystal
configurations and materials used, as known by one of ordinary
skill in the relevant arts, are intended to be included in the
scope of at least a few exemplary embodiments.
[0032] Additionally, referral is made herein of columnar
structures. The columnar structures of a woodpile is one
non-limiting example of a columnar structure, other non-limiting
examples include non-columnar structures, non-uniform
cross-sectional structures, other structures used in photonic
crystals as known by one of ordinary skill in the relevant arts and
equivalents.
[0033] Additionally, the actual size of structures may not be
discussed however any size from micrometer (centimeter to meters)
to nanometer and below sized photonic crystal structures are
intended to lie within the scope of exemplary embodiments (e.g.,
photonic structures with characteristic sizes of individual
molecules, nanometer size, micro size, centimeter, and meter
sizes).
[0034] Additionally, exemplary embodiments are not limited to
visual optical systems; photonic crystal structures can be
constructed for use with infrared and other wavelength systems. For
example an infrared light detector (e.g., a detector measuring
infrared markings).
First Exemplary Embodiment
[0035] FIG. 1 illustrates a schematic representation of a resonator
using a three-dimensional photonic crystal according to a first
exemplary embodiment. The resonator 10 is produced by (i.e.,
includes) a point defect 120 formed in a periodic structure 100 or
three-dimensional photonic crystal. The periodic structure 100 has
a period comprising 12 layers in xy planes from a first layer 101
to a twelfth layer 112. FIG. 2 illustrates the xy sections of the
12 layers. The first layer 101 and the seventh layer 107 each
contain a plurality of columnar structures 101a or 107a that are
formed of a first medium (e.g., having a high refractive index) and
extend in the y-axis direction and are arranged at regular
intervals (lattice period) p in the x-axis direction. The columnar
structures 101a of the first layer 101 are shifted by, for example,
P/2 in the X-axis direction with respect to the columnar structures
107a of the seventh layer 107. The fourth layer 104 and the tenth
layer 110 each contain a plurality of columnar structures 104a or
110a that are formed of a medium (e.g., the first medium) and
extend in the x-axis direction and are arranged at regular
intervals P in the y-axis direction. The columnar structures 104a
of the forth layer 104 are shifted by, for example, P/2 in the
y-axis direction with respect to the columnar structures 110a of
the tenth layer 110. The second layer 102 and the third layer 103,
which define an additional layer, each contain discrete structures
102a or 103a that are formed of the a medium (e.g., the first
medium) and are separately disposed at positions in the xy planes,
corresponding to the intersections of the columnar structures 101a
of the first layer 101 and the columnar structures 104a of the
fourth layer 104. The discrete structures 102a and the discrete
structures 103a can be symmetrically disposed such as to be rotated
at an angle of 90.degree. with respect to each other in the
respective xy planes. Other additional layers, namely, the fifth
layer 105 and sixth layer 106, the eighth layer 108 and ninth layer
109, and the eleventh layer 111 and twelfth layer 112, can each be
disposed between the columnar structure-containing layers. Note
that although additional layers (e.g., 102, 103) are discussed
between each pair of layers (e.g., 101 and 104), other exemplary
embodiments can have one additional layer between one pair of
layers, and not have subsequent additional layers, thus the
discussion herein should not be interpreted to limit the number or
arrangement of additional layers in exemplary embodiments.
[0036] The layers (sublayers of the additional layers) 105, 106,
108, 109, 111, and 112 respectively can contain discrete structures
105a, 106a, 108a, 109a, 111a, and 112a that are formed of the a
medium (e.g., the first medium) and are separately disposed in
positions in the respective xy planes corresponding to the
intersections of their adjacent columnar structure-containing
layers, in the same manner. Note that although the present example
of the first exemplary embodiment discusses the discrete structures
(e.g., 105a) as being made from the first medium, in actuality
there are no such limits on exemplary embodiments. An exemplary
embodiment can have discrete structures made of a medium different
than that from which any of the columnar structures are composed.
The columnar structures in each layer can be in contact with the
discrete structures in the adjacent additional layers. The regions
other than the columnar structures or discrete plates in each layer
are filled with a second medium (e.g., having a low refractive
index). Parameters, such as the refractive indices of the first and
second media, the shapes and intervals of the columnar structures
and discrete structures, and the thicknesses of the layers, are
optimally set so as to produce a wide complete photonic band gap in
a desired frequency region (wavelength region).
[0037] Note that some layers have columnar structures, in the
example of exemplary embodiment 1 discussed, made of the same
medium. This is for illustrative purposes only and the columnar
structures can be made of different materials. For example, each
layer can have columnar structures made of different materials,
some can be made of the same, or even columnar structures within a
layer can be made of different materials.
[0038] Also note that a shift of P/2 is discussed, however various
shift values can be used depending upon the design, and the
discussion herein should not be interpreted to limit the amount of
shifts between layers.
[0039] In the example of a first exemplary embodiment, a medium
(e.g., the first medium) has a refractive index of about 3.3, and
the second medium has a refractive index of about 1. The intervals
between the columnar structures are P; each columnar
structure-containing layer has a thickness, or length in the z
direction, of 0.25.times.P; each discrete-structure-containing
layer has a thickness of 0.05.times.P. Each columnar structure has
a long rectangular solid shape with a height, or length in the z
direction, of 0.25.times.P and a width, or length in the x- or
y-axis direction, of 0.3.times.P. Each discrete structure has a
rectangular solid shape with a thickness, or length in the z
direction, of 0.05.times.P and an xy cross section of 0.4.times.P
by 0.6.times.P. FIG. 4 illustrates a photonic band structure of the
periodic structure 100 calculated by a mathematical method (e.g.,
plane wave expansion method). In FIG. 4, the horizontal axis
represents the wave number vector, that is, the direction in which
electromagnetic waves propagate in the photonic crystal. For
example, K on the horizontal axis represents a wave number vector
parallel to the x-axis direction (or y-axis direction), and X on
the horizontal axis represents a wave number vector in xy planes,
forming an angle of 45.degree. with the x axis (or y axis). The
vertical axis represents the frequency normalized with the lattice
period of the periodic structure. FIG. 4 shows that light entering
from any direction cannot be present in the region indicated by
hatching in the normalized frequency range of 0.34 to 0.42; hence,
a complete photonic band gap is produced in this frequency range.
For example, when the intervals P between the columnar structures
are 0.5 .mu.m, a complete photonic band gap is produced in the
wavelength region of 1.19 to 1.47 .mu.m; when the intervals P are
200 nm, a complete photonic band gap is produced in the wavelength
region of 480 to 590 nm.
[0040] Note that the rectangular discrete structures illustrated in
the example of the first exemplary embodiment are for illustrative,
non-limiting, purposes only. In actuality the shape of the discrete
structures are not limited in exemplary embodiments.
[0041] FIG. 3 illustrates an enlarged view of a region around the
point defect 120. The point defect 120 is formed of a medium (e.g.,
the first medium) in a solid shape (e.g., rectangular) with a
thickness Dz, a length Dx in the x-axis direction, and a length Dy
in the y-axis direction. The point defect 120 facilitates the
presence only therein of electromagnetic waves in a part of the
wavelength region of the photonic band gap of the periodic
structure 100. Thus, electromagnetic waves can be confined in a
very small region, and the point defect 120 can serve as a
high-performance resonator exhibiting a high confinement effect.
The state in which electromagnetic waves are facilitated to be
present in a photonic band gap that is caused by providing the
point defect is hereinafter referred to as a defect mode; the
frequency of the electromagnetic waves in this state is referred to
as a defect mode frequency; and the distribution of electromagnetic
energy in a resonator produced by the point defect is referred to
as a defect mode pattern.
[0042] FIGS. 5 to 7 illustrate how the defect mode frequencies of
the resonator 10 shown in FIG. 1 are changed depending on
parameters of the shape of the point defect 120, according to the
results of calculations by a mathematical method (e.g., the FDTD
(Finite Difference Time Domain) method). FIG. 5 illustrates the
relationship between the defect mode frequencies and length Dx when
the dimensions of the point defect are Dz=0.3.times.P and Dx=Dy.
For example, referring to FIG. 3, the point defect 120 used for the
calculations is formed in two layers containing the columnar
structures 104a and the discrete structures 103a such that the
center coordinates in the x- and y-axis directions of the point
defect 120 are the same as the center coordinates in the x- and
y-axis directions of one of the discrete structures 103a. The
hatched frequency regions in FIG. 5 represent frequencies outside
the complete photonic band gap. FIG. 6 illustrates the relationship
between the defect mode frequencies and length Dy when the
dimensions of the point defect are Dz=0.3.times.P and
Dx=0.8.times.P. For example, referring to FIG. 3, the point defect
120 used for the calculations is formed in two layers containing
the columnar structures 104a and the discrete structures 103a such
that the center coordinates of the point defect 120 in the x- and
y-axis directions are the same as the center coordinates in the x-
and y-axis directions of one of the discrete structures 103a. FIG.
7 illustrates the relationship between the defect mode frequencies
and length Dz when the dimensions of the point defect are
Dx=0.8.times.P and Dy=0.8.times.P. For example, referring to FIG.
3, the point defect 120 used for the calculations is formed such
that its center coordinates in the x- and y-axis directions are the
same as the center coordinates in the x- and y-axis directions of
one of the discrete structures 103a, and such that its minimum
coordinate in the z direction is the same as the minimum coordinate
in the z direction of the columnar structures 104a. The variation
in defect mode frequency for the shape of the point defect depends
on the dimensional parameters. This suggests that the defect mode
frequency can be controlled by varying the shape of the point
defect. The manner of the changes in defect mode frequency for Dz
values is distinguished from the manners of the changes for Dx and
Dy values, as shown in FIGS. 5 to 7. This distinction facilitates
setting the defect mode frequencies with large intervals so that a
designed defect mode frequency can be set with reduced influence of
the adjacent defect modes.
[0043] For example, a single defect mode can be produced in the
photonic band gap, that is, a single mode can be achieved, by
designing the point defect 120 in FIG. 3 at dimensions of Dx=P,
Dy=0.3.times.P, and Dz=0.35.times.P such that its center
coordinates in the x- and y-axis directions are the same as the
center coordinates in the x- and y-axis directions of one of the
discrete structures 103a, and such that its minimum coordinate in
the z direction is the same as the minimum coordinate in the z
direction of the columnar structures 104a. In this instance, the
point defect 120 can be formed in a discrete-structure-containing
layer and its adjacent columnar structure-containing layer. In view
of the manufacturing process, the thickness Dz of the point defect
120 can be related to the sum of the thicknesses of the
discrete-structure-containing layer and the columnar
structure-containing layer. By forming the point defect in a
columnar structure-containing layer and at least one
discrete-structure-containing layer (e.g., where the
discrete-structure-containing layer has a thickness smaller than
that of the columnar structure-containing layer), control of the
defect mode frequency can be facilitated. FIG. 8 illustrates the
spectrum of defect mode frequency of a periodic structure 100
formed at 8 periods in the x- and y-axis directions and 4 periods
in the z direction with the point defect 120 at the center of the
periodic structure, while FIG. 9 illustrates a defect mode pattern
of an xy section of the periodic structure. In FIG. 9, the white
region indicates a higher energy area and the black region
indicates a lower energy area. FIGS. 8 and 9 show that a highly
symmetrical single defect mode can be achieved.
[0044] The Q factor, which represents a property of the light
confinement of a resonator and is defined as the quotient of energy
stored in a resonator divided by energy lost in a unit time from
the resonator, of the defect mode shown in FIG. 8 is about 3,800.
The Q factor is logarithmically increased by increasing the number
of the period of the periodic structure 100. For example, the Q
factor can be increased to about 3.times.10.sup.8 by setting the
number of periods in the x- and y-axis directions at 20P and in the
z direction at 16P. The number of periods of the periodic structure
can be selected from numbers capable of producing a desired
confinement effect.
[0045] Designed defect mode frequencies can be obtained by
designing the periodic structure under controlled conditions for
example by controlling, the refractive indices of the first and
second media, the shapes and intervals of the columnar structures
and the discrete structures, and the thicknesses of the layers, so
that a complete photonic band gap is produced in a frequency region
including the designed defect mode frequency. Where controlled
conditions can be used to form the point defect in at least one
discrete-structure-containing layer at a thickness Dz different
from the thickness of the columnar structure-containing layer. In
at least one exemplary embodiment, the designed defect mode
frequencies can be achieved at desired intervals, with the symmetry
of the defect mode pattern maintained. Thus, the resulting
resonator can be of improved performance and exhibit an improved
light confinement effect. In particular, when the center of the
point defect is positioned on an axis extending in the stacking
direction from the center of an intersection of projections of the
columnar structures, or on an axis extending in the stacking
direction from a position shifted by chosen amount (e.g., P/2) from
the center of an intersection of projections of the columnar
structures in either of the directions in which the columnar
structures are parallely arranged. The structural symmetry of the
region around the point defect can be enhanced and, accordingly,
the symmetry of the defect mode pattern increases, in comparison
with the conventional system described in the background. In
further exemplary embodiments, the defect mode frequencies can be
varied by changing the shape of the defect, facilitating the design
of an increased performance resonator with the designed resonator
frequency.
[0046] In the above description, the center of the point defect is
positioned on an axis extending in the stacking direction of the
layers from the center of an intersection of projections of the
columnar structures, or on an axis extending in the stacking
direction from a position shifted by a chosen amount (e.g., P/2)
from the center of an intersection of projections of the columnar
structures in either of the directions in which the columnar
structures are parallely arranged. In practice, however, the
position of the point defect may have an error of, for example,
about .+-.0.1.times.P with respect to the axis extending in the
stacking direction. Exemplary embodiments include errors in the
positioning of the point defect.
[0047] In at least one exemplary embodiment, the point defect can
be formed in a discrete-structure-containing layer and its adjacent
columnar structure-containing layer. To facilitate control the
defect mode frequencies by varying the thickness of the point
defect, the point defect may be formed in at least one
discrete-structure-containing layer, as illustrated in FIGS. 10A
and 10B, depending on a designed frequency.
[0048] In at least one exemplary embodiment, the adjacent
discrete-structure-containing layers, for example, the second layer
102 and the third layer 103, define an additional layer, and the
layers from the first layer 101 to the twelfth layer 112 define a
unit of the periodic structure 100 (FIG. 1). Alternatively, the
unit of the point defect structure may be defined by at least three
layers including an additional layer and two columnar
structure-containing layers. In this instance, the additional layer
includes at least one discrete-structure-containing layers. For
example, a three-dimensional photonic crystal including a first
layer, a second layer, and an additional layer may be used for a
functional device producing a relatively wide complete photonic
band gap. The first layer includes a plurality of columnar
structures arranged parallel to a first axis at a first
predetermined interval. The second layer includes a plurality of
columnar structures arranged parallel to a second axis at second
predetermined intervals. Where in at least one exemplary embodiment
the first and second predetermined intervals can be substantially
equal. Similarly the third predetermined interval and the fourth
predetermined interval can have the same or different value. The
additional layer includes at least one sublayer containing discrete
structures that can be separately arranged in a plane defined by
the first and second axes. The first layer and the second layer are
separated by the additional layer. The discrete structures can be
disposed at positions corresponding to the intersections of
projections of the columnar structures. By increasing the number of
discrete-structure-containing sublayers in the additional layer,
the width of the photonic band gap can be increased. By use of an
additional layer including at least two
discrete-structure-containing sublayers, the reflectance of
three-dimensional photonic crystal at a defect mode frequency can
be increased, and its directional dependency can be reduced. Thus,
a resonator in accordance with at least one exemplary embodiment
can produce a resonator with an increased light confinement effect
and/or exhibit high performance with a high Q factor. Also, since
the three-dimensional photonic crystal can have a wide photonic
band gap, the defect mode frequencies can be controlled in a wide
range. For example, in at least one exemplary embodiment, the
manufacturing precision is increased by designing the thickness of
the point defect to be substantially equal to the thickness of the
additional layer or the sum of the thicknesses of a columnar
structure-containing layer and its adjacent
discrete-structure-containing layer.
[0049] In exemplary embodiments, the shift of the columnar
structures of the first layer 101 from the columnar structures of
the seventh layer 107 and the shift of the columnar structures of
the fourth layer 104 from the columnar structures of the tenth
layer 110 can be by a chosen amount (e.g., substantially 1/2 of the
interval P between the columnar structures).
[0050] The periodic structure can be formed from at least two media
with a high refractive index ratio. Exemplary high refractive index
media include compound semiconductors such as GaAs, InP, and GaN,
Si and other semiconductors, TiO.sub.2 and similar dielectrics,
metals, and other similar materials as known by one of ordinary
skill in the relevant art and equivalents. Exemplary low refractive
index media include SiO.sub.2 and similar dielectrics, polymers
such as polymethylmethacrylate (PMMA), gases (e.g., air), other
similar materials as known by one of ordinary skill in the relevant
art and equivalents. The photonic band gap of a photonic crystal
results from the distribution of dielectric constants in the
crystal. Combined use of media having an increased dielectric
constant ratio leads to a wider complete photonic band gap. In at
least one exemplary embodiment, the refractive index ratio can be
at least 2. In the above example of the first exemplary embodiment,
a high refractive index medium can be used as the first medium, and
a low refractive index medium can be used as the second medium.
However, medium 1 and medium 2 are not limited to this example, in
accordance with the exemplary embodiment, can have a variety of
refractive index values.
[0051] Although, in the above example of the first exemplary
embodiment, the point defect can be formed of the same medium as
the columnar structures and the discrete structure, the point
defect may be formed of a medium having a different refractive
index as well.
Second Exemplary Embodiment
[0052] FIG. 11 is a schematic illustration of a resonator according
to a second exemplary embodiment. The resonator 20 can include a
point defect 210 provided in a periodic structure 200. The periodic
structure 200 can have a period defined by four (4) layers (each
substantially parallel to the xy plane) from a first layer 201 to a
fourth 204. The first layer 201 and the third layer 203 each can
contain a plurality of columnar structures 201a or 203a (FIG. 12)
that can be formed of a first medium (e.g., having a high
refractive index) so as to extend in the x-axis direction and can
be arranged at regular intervals (lattice period) P in the y-axis
direction. The columnar structures 201a of the first layer 201 can
be shifted, (e.g., P/2 in the y-axis direction) with respect to the
columnar structures 203a of the third layer 203. The second layer
202 and the fourth layer 204 each contain a plurality of columnar
structures (e.g., 202a) that can be formed of the first medium so
as to extend in the y-axis direction and are arranged at regular
intervals P in the x-axis direction. The columnar structures 202a
of the second layer 202 are shifted (e.g., P/2 in the x-axis
direction) with respect to the columnar structures 204a of the
fourth layer 204. The regions other than the columnar structures in
each layer can be filled with a second medium (e.g., having a low
refractive index). Conditions, such as the refractive indices of
the first and second media, the shape and intervals of the columnar
structures, and the thicknesses of the layers, can be set so as to
produce a wide complete photonic band gap in a designed frequency
region (wavelength region). In the example of the second exemplary
embodiment, the refractive index of the first medium is set at
about 3.3, and the refractive index of the second medium is set at
about 1. The intervals between the columnar structures are P. Each
columnar structure has a long rectangular solid shape with a
height, or length in the z direction, of 0.3.times.P and a width,
or length in the x- or y-axis direction, of 0.25.times.P. FIG. 13
illustrates the photonic band structure of the periodic structure
200 calculated by a mathematical method (e.g., plane wave expansion
method). In FIG. 13, the horizontal axis represents the wave number
vector, that is, the direction in which electromagnetic waves
propagate in the photonic crystal. For example, K on the horizontal
axis represents a wave number vector parallel to the x-axis
direction (or y-axis direction), and X on the horizontal axis
represents a wave number vector in xy planes, forming an angle of
45.degree. with the x axis (or y axis). The vertical axis
represents the frequency normalized with the lattice period of the
periodic structure. FIG. 13 shows that light entering from any
direction cannot be present in the region indicated by hatching in
the normalized frequency range of 0.39 to 0.46; hence, a complete
photonic band gap is produced in this frequency range. For example,
when the intervals P between the columnar structures are 0.5 .mu.m,
a complete photonic band gap is produced in the wavelength region
of 1.09 to 1.28 .mu.m; when the intervals P are 250 nm, a complete
photonic band gap is produced in the wavelength region of 540 to
640 nm.
[0053] FIG. 12 is an enlarged view of a region around the point
defect 210. The point defect 210 can be formed of the same medium
as the columnar structures, in the example illustrated the point
defect is a rectangular solid shape with a thickness Dz1, a length
Dx1 in the x-axis direction, and a length Dy1 in the y-axis
direction, so as to partially contain one of the columnar
structures. The point defect 210 facilitates the presence of
electromagnetic waves in a part of the wavelength region of the
photonic band gap of the periodic structure 200. Thus,
electromagnetic waves can be confined in a very small region, and
the point defect 210 can serve as a resonator exhibiting an
improved confinement effect
[0054] FIGS. 14 to 16 show how the defect mode frequencies of the
resonator 20 shown illustrated FIG. 11 are changed depending on
parameters of the shape of the point defect 210, according to the
results of calculations by a mathematical method (e.g., the FDTD
method). FIG. 14 illustrates the relationship between the defect
mode frequencies and length Dx1 when the dimensions of the point
defect are Dz1=0.3.times.P and Dx1=Dy1. For example, referring to
FIG. 12, the point defect 210 used for the measurements is formed
in the layer containing the columnar structures 202a such that the
center coordinate in the x-axis direction of the point defect 210
is the same as the center coordinates in the x-axis direction of
one of the columnar structures 202a, and such that the center
coordinate in the y-axis direction of the point defect 210 is
substantially the same as the center coordinate in the y-axis
direction of one of the columnar structures 201a. The hatched
frequency regions in FIG. 14 are outside the complete photonic band
gap. FIG. 15 illustrates the relationship between the defect mode
frequencies and length Dy1 when the dimensions of the point defect
are Dz1=0.3.times.P and Dx1=0.75.times.P. For example, referring to
FIG. 12, the point defect 210 used for the calculations is formed
in the layer containing the columnar structures 202a such that the
center coordinate in the x-axis direction of the point defect is
substantially the same as the center coordinate in the x-axis
direction of one of the columnar structures 202a, and such that the
center coordinate of the defect in the y-axis direction is the same
as the center coordinate in the y-axis direction of one of the
columnar structures 201a. FIG. 16 illustrates the relationship
between the defect mode frequencies and the thickness Dz1 when the
dimensions of the point defect are Dx1=0.75.times.P and
Dy1=0.375.times.P. For example, referring to FIG. 12, the point
defect 210 used for the measurements is formed such its center
coordinate in the x-axis direction is the same as the center
coordinate in the x-axis direction of one of the columnar
structures 202a, such that the center coordinate in the y-axis
direction of the point defect 210 is substantially the same as the
center coordinate in the y-axis direction of one of the columnar
structures 201a, and such that the maximum coordinate in the z
direction of the point defect 210 is the same as the maximum
coordinate in the z direction of the columnar structure 202a.
[0055] As in the first exemplary embodiment, the complete photonic
band gap of the second exemplary embodiment can produce a frequency
region including a desired defect mode frequency, by controlling
conditions of the second exemplary embodiment, such as the
refractive indices of the first and second media of the periodic
structure, the shape of and interval between the columnar
structures, and the thickness of the layers. In particular, by
controlling the thickness of the point defect 210 where the
thickness Dz1 of the point defect differs from that of the columnar
structures 205, the defect mode frequencies can be controlled in a
wider range, and designed defect mode frequencies can be achieved
at designed intervals, with the symmetry of the defect mode pattern
maintained. The columnar structures and the point defect are not
necessarily formed of the same medium, as in the first exemplary
embodiment.
[0056] For example, a single defect mode can be produced in a
photonic band gap, that is, a single mode can be achieved, by
forming the point defect 210 shown in FIG. 12 to dimensions of
Dx1=0.75.times.P, Dy1=0.375.times.P, and Dz1=0.35.times.P such that
its center coordinate in the x-axis direction is the same as the
center coordinate of one of the columnar structures 202a, such that
the center coordinate in the y-axis direction is the same as the
center coordinate of one of the columnar structures 201a, and such
that its maximum coordinate in the z direction is the same as that
of the columnar structure 202a. Note that the above dimensions for
the point defect 210 are intended for illustration only and not as
limiting factors. Further exemplary embodiments can have various
other dimensions of the point defect. FIG. 17 illustrates the
spectrum of defect mode frequency of a periodic structure 200
formed at 8 periods in the x- and y-axis directions and 4 periods
of the z direction with the point defect 210 at the center of the
periodic structure 200, and FIG. 18 illustrates a defect mode
pattern of an xy section of the periodic structure. FIGS. 17 and 18
show that a highly symmetrical single defect mode pattern has been
achieved.
Third Exemplary Embodiment
[0057] An optical-function device including a resonator according
to exemplary embodiments will now be described. The point defect of
the three-dimensional photonic crystal according to the first or
the second exemplary embodiment can be filled with an active medium
capable of emitting light, and energy, such as electromagnetic
waves or current, when driven by a driver. Thus, an increased
efficient light emitting device, (e.g., a laser, an LED, other
light emitting devices as known by one of ordinary skill in the
relevant arts, and equivalents) can be facilitated. The active
medium can be selected from, for example, materials having a
multi-quantum well structure or multi-quantum dot structure, such
as InGaAsP, AlGaAs, AlGaInP, AlGaN, InGaN, ZnSe, and ZnS, organic
materials, other multi-quantum well or dot structures as known by
one of ordinary skill in the relevant art and equivalents,
according to the designed resonant wavelength. Thus, an increased
efficient laser light source can be achieved which can be suitably
used for displays, optical communications, THz light, and DVD
optical pickups. FIG. 19 illustrates the structure of a laser
device having an active portion that emits light by carrier
injection, in a point defect. The laser device 300 includes a
resonator prepared by forming a point defect 320 in a periodic
structure 310 according to the first or the second exemplary
embodiment, a p-type electrode 331, a p-type carrier conduction
path 330, an n-type electrode 341, an n-type carrier conduction
path 340, and a waveguide 350. The resonator has an active portion
inside that emits light by carrier injection. The waveguide 350 can
be produced by a linear defect that can be formed in the periodic
structure 310 so as to disturb the periodicity. The wavelength of
the waveguide mode can be set so as to increase the combination
efficiency with the resonator, in consideration of the resonance
mode, by varying the shape and refractive index of the linear
defect. The linear defect can be formed by changing the shape or
refractive index of some of the columnar structures in the periodic
structure 310, or by providing an additional columnar structure.
Holes can be supplied to the resonator through the p-type electrode
331 and the p-type carrier conduction path 330, and electrons can
be supplied to the resonator through the n-type electrode 341 and
the n-type carrier conduction path 340. The holes and electrons can
be combined in the resonator to emit light or generate laser light,
and the light can be extracted through the waveguide 350.
[0058] The point defect in the three-dimensional photonic crystal
according to the first or the second exemplary embodiment may be
filled with a nonlinear material, and energy, such as the
electromagnetic waves or current, may be supplied to the nonlinear
material. Since this structure can confine light with a strong
energy in a very narrow region, the resulting nonlinear optical
device can produce increased nonlinear optical effects. The
nonlinear material may be LiNbO.sub.3, LiTaO.sub.3, BaTiO.sub.3,
ZnO, BaB.sub.2O.sub.4, BiB.sub.3O.sub.6, KTiOPO.sub.4, or other
nonlinear material as known by one of ordinary skill in the
relevant art or equivalents. FIG. 20 illustrates a wavelength
conversion device 400 using the nonlinear optical effect. The
wavelength conversion device 400 includes a resonator prepared by
forming a point defect 420 in a periodic structure 410 according to
the first or the second exemplary embodiment, an input waveguide
430, and an output waveguide 440. The inside of the resonator can
be filled with a nonlinear material. The input waveguide 430 and
the output waveguide 440 can each be produced by a linear defect
that can be formed in the periodic structure 410 so as to disturb
the periodicity. The wavelength of the waveguide mode can be
selected according to, for example, the shape and refractive index
of the linear defect. Light introduced into the input waveguide 430
from the outside (e.g., through a lens or a fiber) can be converted
into second or higher harmonics in the resonator. The harmonics are
extracted through the output waveguide 440. The guided wavelength
region of the input waveguide 430 can be set so as to include the
wavelength of the incident light, not including the wavelength of
the converted light, and the guided wavelength region of the output
waveguide 440 can be set so as to include the wavelength of the
converted light, not including the wavelength of the incident
light. Thus, the wavelength of incident light can be efficiently
converted and the converted light can efficiently be extracted.
Light having a plurality of wavelengths may be used. This light can
be converted by use of a nonlinear effect of light other than
harmonics, such as sum of light frequencies or difference frequency
light, and can then be extracted.
[0059] The three-dimensional photonic crystal optical resonators 10
and 20 according to the first and the second exemplary embodiment
can be used as part of wavelength selection filters. The wavelength
selection filters can output light with a frequency with high
selectivity, according to the defect mode.
[0060] Furthermore, the above-described optical functional devices
can be combined to prepare an optical circuit. By sharing the same
periodic structure among the optical functional devices, the size
of the optical circuit can be further reduced.
[0061] Exemplary embodiments can use three-dimensional photonic
crystals with point defects that can serve as a resonator having
designed defect mode frequencies at designed intervals, while
maintaining the symmetry of the defect mode patterns. The resonator
can be of increased performance and exhibits an increased light
confinement effect over some conventional systems. By use of the
resonator in a laser, the laser can oscillate at a desired
wavelength with high efficiency. The resonator according to the
present invention can achieve highly functional optical
devices.
[0062] Exemplary embodiments are capable of being used in many
devices, for example in light emitting devices and wavelength
conversion devices.
[0063] While the present invention has been described with
reference to exemplary embodiments, it is to be understood that the
invention is not limited to the disclosed embodiments. The scope of
the following claims is to be accorded the broadest interpretation
so as to encompass all modifications and equivalent structures and
functions. For example, in the interest of acting as ones own
lexicographer, although the following claims cite terms such as
"direction perpendicular", the intended meaning of these terms
within the scope of the claims is to include arrangements where the
"direction is substantially perpendicular" or "essentially
perpendicular." Additionally, the term "plane parallel" is intended
to include arrangements where the "plane is essentially parallel."
For example the intended scope is perpendicular or parallel within
a variance of the true perpendicular or parallel position (e.g.,
with a few degrees inclination). Likewise the phrase "layer are
orthogonal" is intended to include arrangements where the "layer is
substantially orthogonal" and the term "extending in the same
direction" is intended to include the arrangements "extending in
about the same direction." For example the intended scope is meant
to include the same direction and orthogonal within a variance of
the true same direction or orthogonal position (e.g., a few degrees
inclination). Finally the term "one-half of" is intended to include
arrangements of "about one-half" (i.e., one-half within a variance
(e.g., 1% of 1/2)).
[0064] This application claims priority from Japanese Application
No. 2004-301374 filed Oct. 15, 2004, which is hereby incorporated
by reference herein in its entirety.
* * * * *